Weight assignment method for multiple attribute decision making with dissimilarity and conflict of belief distributions

Belief distribution (BD) is the scheme of representing uncertain and imprecise subjective assessment in the evidential reasoning methodology. In a multiple attribute decision making (MADM) problem, how to elicit attribute weights rationally from subjective assessments is an open issue. Moreover, the support degree of assessment for the final decision is critically important because it has a direct implication on the likelihood of making a right decision. The aim of this paper is firstly to identify the intrinsic information carried by different attributes in the form of BDs for generating attribute weights in a MADM problem. Thus, we present the concept of conflict measure between two attributes on both the alternative and evaluation grade level. A novel weight assignment method is further proposed based on the conflict measure between attributes and the divergence of different BDs. Secondly, the paper puts forward the external divergence and internal indeterminacy to measure the support degree of the final aggregated results for decision making. They are determined by the defined concept of dissimilarity and uncertainty measures on alternatives. A series of properties and comparative analysis are given to demonstrate the rationality and effectiveness of the proposed methods.